3x(4x+2)=130

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Solution for 3x(4x+2)=130 equation:


Simplifying
3x(4x + 2) = 130

Reorder the terms:
3x(2 + 4x) = 130
(2 * 3x + 4x * 3x) = 130
(6x + 12x2) = 130

Solving
6x + 12x2 = 130

Solving for variable 'x'.

Reorder the terms:
-130 + 6x + 12x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + 6x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-65 + 3x + 6x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-65 + 3x + 6x2)' equal to zero and attempt to solve: Simplifying -65 + 3x + 6x2 = 0 Solving -65 + 3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10.83333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '10.83333333' to each side of the equation. -10.83333333 + 0.5x + 10.83333333 + x2 = 0 + 10.83333333 Reorder the terms: -10.83333333 + 10.83333333 + 0.5x + x2 = 0 + 10.83333333 Combine like terms: -10.83333333 + 10.83333333 = 0.00000000 0.00000000 + 0.5x + x2 = 0 + 10.83333333 0.5x + x2 = 0 + 10.83333333 Combine like terms: 0 + 10.83333333 = 10.83333333 0.5x + x2 = 10.83333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 10.83333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 10.83333333 + 0.0625 Combine like terms: 10.83333333 + 0.0625 = 10.89583333 0.0625 + 0.5x + x2 = 10.89583333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 10.89583333 Calculate the square root of the right side: 3.30088372 Break this problem into two subproblems by setting (x + 0.25) equal to 3.30088372 and -3.30088372.

Subproblem 1

x + 0.25 = 3.30088372 Simplifying x + 0.25 = 3.30088372 Reorder the terms: 0.25 + x = 3.30088372 Solving 0.25 + x = 3.30088372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 3.30088372 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.30088372 + -0.25 x = 3.30088372 + -0.25 Combine like terms: 3.30088372 + -0.25 = 3.05088372 x = 3.05088372 Simplifying x = 3.05088372

Subproblem 2

x + 0.25 = -3.30088372 Simplifying x + 0.25 = -3.30088372 Reorder the terms: 0.25 + x = -3.30088372 Solving 0.25 + x = -3.30088372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -3.30088372 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.30088372 + -0.25 x = -3.30088372 + -0.25 Combine like terms: -3.30088372 + -0.25 = -3.55088372 x = -3.55088372 Simplifying x = -3.55088372

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.05088372, -3.55088372}

Solution

x = {3.05088372, -3.55088372}

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